It is well known that the Onsager reciprocal relations give important identities
between transport coefficients for heat and charge conduction
in the linear response regime. [1]}, [2]} For example, the Peltier coefficient \(\Pi \)  is
related to the Seebeck coefficient \(S\)  in a simple form as \(S = \Pi /T\) , where \(T\)  is the temperature.
The Onsager-Casimir symmetry, which is the extension of the Onsager relation in the presence
of an external magnetic field, is also derived from the microscopic reversibility. [3]}
Recently, a general relation called the steady-state fluctuation theorem has been derived
by the same concept of the microscopic reversibility. [4]}, [5]}
It gives an identity equation on the probability of the entropy production \(\Delta S\)  during time \(\tau \)  as
\(\ln \left[ \frac{P(\Delta S)}{P(-\Delta S)} \right] = \Delta S,\) 
